Distribution shifts naturally arise in real-world settings, particularly when environments with low overlap interact so that even though sub-groups share some common features, they can differ substantially in some other locale-specific features [1]}. In such settings, the partial invariance framework can better tackle the OOD problem. Similar notions can also be found in recent literature pertaining to equivariant neural networks, in relaxing global symmetry requirements to local gauge symmetries[2]}.
